Divide the following complex numbers: $\dfrac{8 e^{19\pi i / 12}}{4 e^{3\pi i / 4}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8 e^{19\pi i / 12}$ ) has angle $\frac{19}{12}\pi$ and radius 8. The second number ( $4 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius 4. The radius of the result will be $\frac{8}{4}$ , which is 2. The angle of the result is $\frac{19}{12}\pi - \frac{3}{4}\pi = \frac{5}{6}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{5}{6}\pi$.